A327188 For any n >= 0: consider the different ways to split the binary representation of n into two (possibly empty) parts, say with value x and y; a(n) is the greatest possible value of x AND y (where AND denotes the bitwise AND operator).

0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 3, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 2, 4, 4, 4, 4, 0, 1, 2, 2, 4, 5, 4, 5, 0, 1, 2, 3, 4, 4, 6, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 2, 4, 4, 4, 4, 0, 1, 2, 2, 4, 4, 4, 4, 0, 1, 2, 2, 4, 5, 4

Offset: 0

Author

Rémy Sigrist, Aug 25 2019

Keywords

• nonn
• look
• base

Comments

The first 10000 positive integers where the sequence equals zero match the first 10000 terms of A082662; is that true forever?

Examples

			For n=42:
- the binary representation of 42 is "101010",
- there are 7 ways to split it:
   - "" and "101010": x=0 and y=42: 0 AND 42 = 0,
   - "1" and "01010": x=1 and y=10: 1 AND 10 = 0,
   - "10" and "1010": x=2 and y=10: 2 AND 10 = 2,
   - "101" and "010": x=5 and y=2: 5 AND 2 = 0,
   - "1010" and "10": x=10 and y=2: 10 AND 2 = 2,
   - "10101" and "0": x=21 and y=0: 21 AND 0 = 0,
   - "101010" and "": x=42 and y=0: 42 AND 0 = 0,
- hence a(42) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192

Crossrefs

See A327186 for other variants.

Cf. A082662.

Programs

PARI

a(n) = my (v=-oo, b=binary(n)); for (w=0, #b, v=max(v, bitand(fromdigits(b[1..w],2), fromdigits(b[w+1..#b],2)))); v